Q25 of 66 Page 91

Fill in the blanks of the following

If |z + 4| ≤ 3, then the greatest and least values of |z + 1| are ……… and …….

Given |z + 4| ≤ 3


For greatest value of |z + 1|,


⇒ |z + 1| = |z + 4 – 3|


⇒ |z + 1| ≤ |z + 4 – 3|


⇒ |z + 1| ≤ 3 + 3


⇒ |z + 1| ≤ 6


So, greatest value of |z + 1| is 6.


We know that least value of the modulus of a complex number is zero.


So, the least value of |z + 1| is zero.


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